Chapter 3 Time Value of Money Part 2  Learning Objectives  Explain and Illustrate an Annuity  Determine Future Value of an Annuity  Determine Present Value of an Annuity Present Value of Annuity Stream  Adjust formulas for Annuity Due  Distinguish between different loan types  Build an Amortization Schedule  Calculate Waiting Time and Interest Rates for an Annuity

Future Value of Stream of Payments  Different Amounts at Different Times  Use FV formula over and over  Add up each value for Future Value  Note money can only be “added” at same point in time  Is there a short-cut? Sometimes…yes  Annuity Stream  Same amount at same interval

Future Value of Multiple Cash Flow  Same Amount each time and same time interval between each cash flow  Shortcut – Annuity Stream Evaluation  Visualize with time line – page 47

Future Value of Multiple Cash Flow  Three methods again for finding FV  Formula or Equation Method  Calculator Method  Spreadsheet Method  Example 3.1 Scholarship for Lisa  $1,500 annual payment into scholarship fund  Earns 7% interest over 18 years  FV is approximately $51,000

Present Value of Annuity Stream  A similar shortcut for present value  Three methods but basic same equation

Ordinary Annuity versus Annuity Due  Need to visualize the difference between an annuity at the start of the period versus and annuity at the end of a period  Start of Period – Annuity Due  Example rent payment  End of Period – Ordinary Annuity  Example car payment  Original Formulas for Ordinary Annuity  Adjustment for Annuity Due – multiply by (1+r)

Perpetuities  Never Ending Annuity Stream  How can you handle an infinite number of payments?  Formula reduces to:

Amortization Schedule  Typical consumer loans make equal payments every period  What is the balance (principal) at the end of any month if some of the payment is for interest and some for principal reduction?  Amortization Schedule shows each payments application to interest expense and principal reduction

Three Payment Methods  All loans contain a repayment of the original amount (principal) and cost of borrowed money (interest)  Types of repayment  Interest and Principal at Maturity  Interest as you go, Principal at Maturity  Interest and Principal as you go  Why the difference in interest? Table 3.1

Amortization Schedule  How to build an amortization schedule  Step One – Determine the payment for each period given number of periods (n), interest rate (r), and the present value (PV).  Step Two – Determine each periods required interest payment  Outstanding Balance x Interest rate = Interest expense  Step Three – Determine principal reduction  Payment – Interest expense = Principal Reduction  Step Four – Determine remaining principal  Beginning of Period Principal – Principal reduction = End of Period Principal  Step Five – Repeat Steps Two through Four, n-1 times

Waiting Time  Same shortcut for Waiting Time, find n with an annuity stream

Finding Interest Rates with Annuities  Interest Rate with Annuities  Can not isolate interest rate variable  Must use an iterative process  Try one interest rate and see if it works…  Try another interest rate and see if it works…  Keep going until you find the correct interest rate.  OR  Use a calculator or spreadsheet and let it do the iterative process

Homework  Problem 9 – Lease versus Buy with TVM  Problem 15 – Future Value  Problem 17 – Present Value  Problem 20 – Payments  Problem 25 – Amortization Schedule